Title: Firing rate model for brain rhythms controlled by astrocytes

Abstract: We propose a new mean-field model of brain rhythms governed by astrocytes. This theoretical framework describes how astrocytes can regulate neuronal activity and contribute to the generation of brain rhythms. The model describes at the population level the interactions between two large groups of excitatory and inhibitory neurons. The excitatory population is governed by astrocytes via a so-called tripartite synapse. This approach allows us to describe how the interactions between different groups of neurons and astrocytes can give rise to various patterns of synchronized activity and transitions between them. Using methods of nonlinear analysis we show that astrocytic modulation can lead to a change in the period and amplitude of oscillations in the populations of neurons.